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Rare events and breakdown of simple scaling in the Abelian sandpile

M. De Menech·A. L. Stella·C. Tebaldi
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Abstract

Due to intermittency and conservation, the Abelian sandpile in 2D obeys multifractal, rather than finite size scaling. In the thermodynamic limit, a vanishingly small fraction of large avalanches dominates the statistics and a constant gap scaling is recovered in higher moments of the toppling distribution. Thus, rare events shape most of the scaling pattern and preserve a meaning for effective exponents, which can be determined on the basis of numerical and exact results.

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M. De Menech, A. L. Stella, C. Tebaldi. 1998-07-16. Rare events and breakdown of simple scaling in the Abelian sandpile. https://doi.org/10.1103/physreve.58.r2677

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